Q)calculate the maximum stress induced in a cast iron pipe of external diameter 40 mm, internal diameter 20 mm and length 4 m when the pipe is supported at its ends and carries a point load of 80 n at the centre.

 Q)calculate the maximum stress induced in a cast iron pipe of external diameter 40 mm, internal diameter 20 mm and length 4 m when the pipe is supported at its ends and carries a point load of 80 n at the centre.

Given, external diameter D = 40 mm.

internal diameter d = 20 mm.

length of pipe l = 4000 mm

centre point load p (80N)

1) moment of inertia for hollow circular section 

I=π/64 (D4-d4)

I = π/64 (40^4 -20^4)

I = π/64 (2560000 - 160000)

I = π/64 * (2400000)

I = π * 2400000/64

= 117809.724 mm4

2) Maximum bending moment for simply supported beam with central point load

M=PL/4

80*4000/4

=8000n/mm

3) Distance from neutral axis to outer fibre (C)

C=D/2

40/2

20 mm

4) Maximum bending stress

σ = MC/I

= 80000*20/117809.7

= 1600000/117809.7 

= 13.58kn/mm2